Over the past several years, code-division multiple access (CDMA) systems have gained widespread interest in the mobile wireless communications field. Both a wide band code division multiple access (WCDMA) and a narrow band code division multiple access CDMA system have been presented. The WCDMA uses a wider channel compared to the narrow band system, which improves frequency diversity effects and therefore reduces fading problems.
The modulation method in CDMA systems is quadrature amplitude modulation QAM. This term is used to describe the combining of two amplitude and phase modulated carriers in quadrature. Quadrature refers to a phase difference of 90 degrees between the two carriers. One of the carriers is known as the In Phase carrier and the other as the Quadrature carrier. One carrier can be a digitally modulated sine wave, while the other carrier is a digitally modulated cosine wave of the same frequency. Thus, the task of every QAM modulator is to perform a circular rotation of [I(n), Q(n)].
FIG. 1 illustrates a digital modulator on a WCDMA system. Spread and scrambled complex-valued physical channels are combined in adder 10 using complex addition. The result is a complex-valued chip sequence that is applied to splitter 11. The splitter splits the complex-valued chip sequence into two parallel branches. The signals in the upper branch and in the lower branch are real-valued signals. Usually the signal in the upper branch is denoted as I signal and the signal in the lower branch is denoted as Q signal.
The modulation is QPSK (Quadrature Phase Shift Keying), wherein the I signal is multiplied in a multiplier 14 with a cosine signal having frequency fL and the Q signal is multiplied in a multiplier 15 with a sine signal having the same frequency fL. Then the resulting signals are summed in a summing element 16 wherein the sum signal is the output signal of the modulator. Usually both the I signal and the Q signal are shaped in shaping filters (not shown).
FIG. 2 depicts a constellation point of an I-signal and a Q-signal represented on a 2-dimensional plane. This plane is called the In phase and Quadrature plane, shortly as the I-Q plane. As seen from the figure, the distance of the constellation point from the origin can be seen as the top end of the vector that is formed from two components, namely the Q component and the I component. The position of the constellation point on the I-Q plane, i.e. the length and the angle of the vector, depends on the I and Q values which, on the other hand, depend on the modulation scheme used.
When the continuous output signal of the modulator is denoted as s(t), the I-signal is denoted as I(n) and the Q-signal is denoted as Q(n), the output signal can be expressed according to the following formula:s(t)=I(n)cos(ωt)+Q(n)sin(ωt)  (1)The maximum amplitude of the output signal s(t) ismax{s(t)}=√{square root over (I(n)2+Q(n)2)}{square root over (I(n)2+Q(n)2)}.  (2)
Note: this is the same as the length of the vector shown in FIG. 2.
In a digital domain the points of the amplitudes of a digitally modulated signal form constellation points on the I-Q plane. Constellation of the signal points on the I-Q plane has a great effect on the signal-to-noise (S/N) ratio and transmission error rate. The transmission error rate depends on the distance between the signal points. If the distance is too small, a signal point adjacent to the true signal point may be extracted erroneously in the receiver. On the other hand, the shape of the constellation affects the operation of the transmitter. It is known in the art that the power of a modulated signal based on a signal point in the I-Q plane is proportional to the square of the distance between the signal point and the origin of the I-Q plane. In other words, the farther the signal point is from the origin, the higher is the power of the modulated signal corresponding to that point.
For several reasons the constellation points of a real modulator are not optimal, usually some output vectors are too extensive. Therefore, in prior art modulators' output vectors must be clipped in some way.
A straightforward way is simply to shorten the output vectors that are too long. The task is to limit the amplitude of the two-dimensional vector to a certain value and retain its original direction. Generally this means that the amplitude of the vector has to be calculated first and if it exceeds the limit, the original vector will be scaled. This procedure consists of operations as multiplication, square root and division, which are very difficult to implement efficiently using digital logic like ASICs or FPGAs or digital signal processors DSPs. This means that approximate methods must be used. However, this causes inaccuracy because, due to features of digital logic, it is difficult to maintain direction of the original vector.
FIG. 3 depicts a rectangular constellation of the signal points of a 64-level modulation scheme. In this example, each point in the constellation represents a modulation symbol comprised of a unique combination of six bits. Points along the horizontal axis represent all possible modulations of a single cosine carrier, whereas points along the vertical axis represent all possible modulations of a single sine carrier. This kind of constellation can be achieved by so-called square clipping where each vector component x, y, is limited (clipped) independently.rresult=xresultex+yresultey,
where                               x          result                =                  {                                                                                                                                        -                                                  r                          limit                                                                    ,                                              x                        <                                                  -                                                      r                            limit                                                                                                                                                                                                          x                      ,                                                                                                  x                                                                          ≤                                                  r                          limit                                                                                                                                                                                                        r                        limit                                            ,                                              x                        >                                                  r                          limit                                                                                                                                ⁢                                                           ⁢              and              ⁢                                                           ⁢                              y                result                                      =                          {                                                                                                                  -                                                  r                          limit                                                                    ,                                              y                        <                                                  -                                                      r                            limit                                                                                                                                                                                                          y                      ,                                                                                                  y                                                                          ≤                                                  r                          limit                                                                                                                                                                                                        r                        limit                                            ,                                              y                        >                                                  r                          limit                                                                                                                                                                            (        3        )            
In the formulas ex is the unit vector of the Q axis and ey is the unit vector of I axis.
This clipping is very easy to implement with hardware but its quality is not very good. The amplitude error is in the range 0≦G<20 log√{square root over (2)} dB≈3 dB and the angle error is limited to |θ|<45°.
However, the rectangular constellation is an unfavorable form because the signal points on the corners reside far from the origin. Those signal points, like signal point 1 in FIG. 3, have the greatest energy. Therefore, it is known to arrange the constellation to form a hexagonal shape, which is depicted by a dotted line in FIG. 3.
The optimal form of the constellation would be a circle, minimizing the average energy per symbol. The effect of the circular constellation is 0.7 dB in comparison to the hexagonal form and around 3 dB in comparison to the rectangular form. Unfortunately, arranging the constellation in a circle is difficult to implement in the praxis and the improvement in the effectiveness increases greatly the complexity of the modulator.
However, when the rectangular or hexagonal constellation shapes are used, the output of the transmitter is prone to saturation due to the high-power modulated signals in the corners. For that reason, the maximum output power of the transmitter is to be limited in accordance with the corner points. Therefore, the output power of the other points is not as high as the transmitter would allow. Consequently, the capacity of the transmitter is not used optimally. Nevertheless, the rectangular constellation is widely used but with a power control circuit to which the output signal of the modulator is applied. This diminishes the drawbacks caused by the constellation shape.
A drawback of the prior art methods is the difficulty to limit the peak transmission power of the transmitter. Limitation using rectangular or hexagonal constellation is in praxis very difficult because it must be based on a trial and error method. Another drawback is the difficulty in maintaining the original direction of the vector. Known methods require relatively complex implementations.